So let's be blunt. Fire/Poison loses out to both Rain and Sand. And CAP3 isn't going to be so fantastic that all of a sudden CAP3 makes Sun the dominant weather.
So we need to decide which Pokemon often on Rain and Sand teams CAP3 should be capable of beating. Obviously, not Politoed or Tyranitar.
But for example do we want Gliscor to be a counter or even a check of CAP3? It obviously has 4X effective STAB EQ and is very bulky. But that would be irrelevant if CAP3 is faster and has good Special Attack + Ice Beam.
I think CAP3 has plenty of defensive checks and counters by virtue of typing, especially once you factor in Rain or Sand. Jellicent, Tentacruel, Politoed, Tyranitar, Gastrodon, Heatran, and Terrakion stand out as the main things.
In large part CAP3 just won't be able to deal with any of those Pokemon without giving CAP3 something specifically designed for that particular counter/check.
The key question to ask is whether a Pokemon countered by such a various list of threats can function. I think no. Therefore, we've got to decide which threats listed by typing alone we want to be eliminated from the list.
The easy way to knock off a huge chunk of the list is to give CAP3 Dry Skin. BUT! I am adamantly opposed to that as it removes Fire/Poison from the "bad typing category."
Instead, I think the easiest thing to do is to remove a few individual threats with individual considerations. Like for example Earthquake helping to remove Heatran (though no help if balloon) and to a lesser degree Tentacruel, Tyranitar, and Terrakion.
I think keeping most (but not all) of these threats as threats is essential. We don't want to make this into something with amazing potential from the get go. That's against concept.